Solve for $x$ and $y$ using elimination. ${6x-4y = 28}$ ${-5x+5y = -15}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $4$ ${30x-20y = 140}$ $-20x+20y = -60$ Add the top and bottom equations together. $10x = 80$ $\dfrac{10x}{{10}} = \dfrac{80}{{10}}$ ${x = 8}$ Now that you know ${x = 8}$ , plug it back into $\thinspace {6x-4y = 28}\thinspace$ to find $y$ ${6}{(8)}{ - 4y = 28}$ $48-4y = 28$ $48{-48} - 4y = 28{-48}$ $-4y = -20$ $\dfrac{-4y}{{-4}} = \dfrac{-20}{{-4}}$ ${y = 5}$ You can also plug ${x = 8}$ into $\thinspace {-5x+5y = -15}\thinspace$ and get the same answer for $y$ : ${-5}{(8)}{ + 5y = -15}$ ${y = 5}$